Design of selective lowpass sampled‐data and digital filters exhibiting equiripple amplitude and phase error characteristics

Abstract

SUMMARYA method is presented for the design of reciprocal reactant sampled-data and digital filters exhibiting equiripple passband and stopband amplitude characteristics and approximating a linear phase characteristic such that the phase error response is equiripple too. The passband amplitude characteristic approximates unity transmission and the stopband amplitude characteristic approximates zero. Odd-and even-degree cases are considered separately. The stopband amplitude response is controlled by an arbitrary number of finite transmission zeros together with two (one) zeros at infinity for even (odd) transfer functions. All the available degrees of freedom are used for controlling the filter performances. Thus the resulting solutions are selective and have good amplitude and phase characteristics. A comparison between our method and a recently published method shows that this approach has higher stopband loss and smaller phase error ripple with wider bandwidth.

FIR filter design problems of simultaneous approximation of magnitude and phase and magnitude and group delay

“…Hence it is natural that one has used (approximate) maximum norm solutions of problem 1 as 563 substitutes for solutions of the third problem (cf. References [16][17][18][19][20][21][22], and see Reference [2] for the relations between these). Also, a linearization of the group delay response of the ÿlter has been used in order to control the group delay in connection with the frequency response problem [19] and to approximately solve problem 4 for small phase errors [6; 23].…”